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Negreiros Lecture II
General Relativity and Neutron Stars - II Rodrigo Negreiros – UFF - Brazil Outline • Compact Stars • Spherically Symmetric • Rotating Compact Stars • Magnetized Compact Stars References for this lecture Compact Stars • Relativistic stars with inner structure • We need to solve Einstein’s equation for the interior as well as the exterior Compact Stars - Spherical • We begin by writing the following metric • Which leads to the following components of the Riemman curvature tensor Compact Stars - Spherical • The Ricci tensor components are calculated as • Ricci scalar is given by Compact Stars - Spherical • Now we can calculate Einstein’s equation as 휇 • Where we used a perfect fluid as sources ( 푇휈 = 푑푖푎푔(휖, 푃, 푃, 푃)) Compact Stars - Spherical • Einstein’s equation define the space-time curvature • We must also enforce energy-momentum conservation • This implies that • Where the four velocity is given by • After some algebra we get Compact Stars - Spherical • Making use of Euler’s equation we get • Thus • Which we can rewrite as Compact Stars - Spherical • Now we introduce • Which allow us to integrate one of Einstein’s equation, leading to • After some shuffling of Einstein’s equation we can write Summary so far... Metric Energy-Momentum Tensor Einstein’s equation Tolmann-Oppenheimer-Volkoff eq. Relativistic Hydrostatic Equilibrium Mass continuity Stellar structure calculation Microscopic Ewuation of State Macroscopic Composition Structure Recapitulando … “Feed” with diferente microscopic models Microscopic Ewuation of State Macroscopic Composition Structure Compare predicted properties with Observed data. Rotating Compact Stars • During its evolution, compact stars may acquire high rotational frequencies (possibly up to 500 hz) • Rotation breaks spherical symmetry, increasing the degrees of freedom. -
Exploring Pulsars
High-energy astrophysics Explore the PUL SAR menagerie Astronomers are discovering many strange properties of compact stellar objects called pulsars. Here’s how they fit together. by Victoria M. Kaspi f you browse through an astronomy book published 25 years ago, you’d likely assume that astronomers understood extremely dense objects called neutron stars fairly well. The spectacular Crab Nebula’s central body has been a “poster child” for these objects for years. This specific neutron star is a pulsar that I rotates roughly 30 times per second, emitting regular appar- ent pulsations in Earth’s direction through a sort of “light- house” effect as the star rotates. While these textbook descriptions aren’t incorrect, research over roughly the past decade has shown that the picture they portray is fundamentally incomplete. Astrono- mers know that the simple scenario where neutron stars are all born “Crab-like” is not true. Experts in the field could not have imagined the variety of neutron stars they’ve recently observed. We’ve found that bizarre objects repre- sent a significant fraction of the neutron star population. With names like magnetars, anomalous X-ray pulsars, soft gamma repeaters, rotating radio transients, and compact Long the pulsar poster child, central objects, these bodies bear properties radically differ- the Crab Nebula’s central object is a fast-spinning neutron star ent from those of the Crab pulsar. Just how large a fraction that emits jets of radiation at its they represent is still hotly debated, but it’s at least 10 per- magnetic axis. Astronomers cent and maybe even the majority. -
Neutron Stars
Chandra X-Ray Observatory X-Ray Astronomy Field Guide Neutron Stars Ordinary matter, or the stuff we and everything around us is made of, consists largely of empty space. Even a rock is mostly empty space. This is because matter is made of atoms. An atom is a cloud of electrons orbiting around a nucleus composed of protons and neutrons. The nucleus contains more than 99.9 percent of the mass of an atom, yet it has a diameter of only 1/100,000 that of the electron cloud. The electrons themselves take up little space, but the pattern of their orbit defines the size of the atom, which is therefore 99.9999999999999% Chandra Image of Vela Pulsar open space! (NASA/PSU/G.Pavlov et al. What we perceive as painfully solid when we bump against a rock is really a hurly-burly of electrons moving through empty space so fast that we can't see—or feel—the emptiness. What would matter look like if it weren't empty, if we could crush the electron cloud down to the size of the nucleus? Suppose we could generate a force strong enough to crush all the emptiness out of a rock roughly the size of a football stadium. The rock would be squeezed down to the size of a grain of sand and would still weigh 4 million tons! Such extreme forces occur in nature when the central part of a massive star collapses to form a neutron star. The atoms are crushed completely, and the electrons are jammed inside the protons to form a star composed almost entirely of neutrons. -
Moons Phases and Tides
Moon’s Phases and Tides Moon Phases Half of the Moon is always lit up by the sun. As the Moon orbits the Earth, we see different parts of the lighted area. From Earth, the lit portion we see of the moon waxes (grows) and wanes (shrinks). The revolution of the Moon around the Earth makes the Moon look as if it is changing shape in the sky The Moon passes through four major shapes during a cycle that repeats itself every 29.5 days. The phases always follow one another in the same order: New moon Waxing Crescent First quarter Waxing Gibbous Full moon Waning Gibbous Third (last) Quarter Waning Crescent • IF LIT FROM THE RIGHT, IT IS WAXING OR GROWING • IF DARKENING FROM THE RIGHT, IT IS WANING (SHRINKING) Tides • The Moon's gravitational pull on the Earth cause the seas and oceans to rise and fall in an endless cycle of low and high tides. • Much of the Earth's shoreline life depends on the tides. – Crabs, starfish, mussels, barnacles, etc. – Tides caused by the Moon • The Earth's tides are caused by the gravitational pull of the Moon. • The Earth bulges slightly both toward and away from the Moon. -As the Earth rotates daily, the bulges move across the Earth. • The moon pulls strongly on the water on the side of Earth closest to the moon, causing the water to bulge. • It also pulls less strongly on Earth and on the water on the far side of Earth, which results in tides. What causes tides? • Tides are the rise and fall of ocean water. -
College of Arts and Sciences
College of Arts and Sciences ANNUAL REPORT 2004·05 awards won · books published · research findings announced programs implemented · research · teaching · learning new collaborations · development of promising initiatives preparation · dedication · vision ultimate success 1 Message from the Dean . 3 Arts and Sciences By the Numbers . 6 Highlights Education . 8 Research . 12 Public Events . 15 Faculty Achievements . 17 Grants . 20 Financial Resources . 22 Appendices . 23 Editor: Catherine Varga Printing: Lake Erie Graphics 2 MESSAGE FROM THE DEAN I have two stories to tell. The first story is a record of tangible accomplishments: awards won, books published, research findings announced, programs implemented. I trust that you will be as impressed as I am by the array of excellence—on the part of both students and faculty—on display in these pages. The second story is about achievements in the making. I mean by this the ongoing activity of research, teaching, and learning; the forging of new collaborations; and the development of promising initiatives. This is a story of preparation, dedication, and vision, all of which are essential to bringing about our ultimate success. 3 As I look back on 2004-05, several examples of achievement and visionary planning emerge with particular clarity: Faculty and Student Recruitment. The College undertook a record number of faculty searches in 2004-05. By tapping the superb networking capabili- ties developed under the leadership of chief informa- SAGES. Under the College’s leadership, SAGES com- tion officer Thomas Knab, our departments were pleted its third year as a pilot program and prepared able to extend these searches throughout the world, for full implementation in fall 2005. -
R-Process Elements from Magnetorotational Hypernovae
r-Process elements from magnetorotational hypernovae D. Yong1,2*, C. Kobayashi3,2, G. S. Da Costa1,2, M. S. Bessell1, A. Chiti4, A. Frebel4, K. Lind5, A. D. Mackey1,2, T. Nordlander1,2, M. Asplund6, A. R. Casey7,2, A. F. Marino8, S. J. Murphy9,1 & B. P. Schmidt1 1Research School of Astronomy & Astrophysics, Australian National University, Canberra, ACT 2611, Australia 2ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia 3Centre for Astrophysics Research, Department of Physics, Astronomy and Mathematics, University of Hertfordshire, Hatfield, AL10 9AB, UK 4Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 5Department of Astronomy, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden 6Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, D-85741 Garching, Germany 7School of Physics and Astronomy, Monash University, VIC 3800, Australia 8Istituto NaZionale di Astrofisica - Osservatorio Astronomico di Arcetri, Largo Enrico Fermi, 5, 50125, Firenze, Italy 9School of Science, The University of New South Wales, Canberra, ACT 2600, Australia Neutron-star mergers were recently confirmed as sites of rapid-neutron-capture (r-process) nucleosynthesis1–3. However, in Galactic chemical evolution models, neutron-star mergers alone cannot reproduce the observed element abundance patterns of extremely metal-poor stars, which indicates the existence of other sites of r-process nucleosynthesis4–6. These sites may be investigated by studying the element abundance patterns of chemically primitive stars in the halo of the Milky Way, because these objects retain the nucleosynthetic signatures of the earliest generation of stars7–13. -
Introduction to Astronomy from Darkness to Blazing Glory
Introduction to Astronomy From Darkness to Blazing Glory Published by JAS Educational Publications Copyright Pending 2010 JAS Educational Publications All rights reserved. Including the right of reproduction in whole or in part in any form. Second Edition Author: Jeffrey Wright Scott Photographs and Diagrams: Credit NASA, Jet Propulsion Laboratory, USGS, NOAA, Aames Research Center JAS Educational Publications 2601 Oakdale Road, H2 P.O. Box 197 Modesto California 95355 1-888-586-6252 Website: http://.Introastro.com Printing by Minuteman Press, Berkley, California ISBN 978-0-9827200-0-4 1 Introduction to Astronomy From Darkness to Blazing Glory The moon Titan is in the forefront with the moon Tethys behind it. These are two of many of Saturn’s moons Credit: Cassini Imaging Team, ISS, JPL, ESA, NASA 2 Introduction to Astronomy Contents in Brief Chapter 1: Astronomy Basics: Pages 1 – 6 Workbook Pages 1 - 2 Chapter 2: Time: Pages 7 - 10 Workbook Pages 3 - 4 Chapter 3: Solar System Overview: Pages 11 - 14 Workbook Pages 5 - 8 Chapter 4: Our Sun: Pages 15 - 20 Workbook Pages 9 - 16 Chapter 5: The Terrestrial Planets: Page 21 - 39 Workbook Pages 17 - 36 Mercury: Pages 22 - 23 Venus: Pages 24 - 25 Earth: Pages 25 - 34 Mars: Pages 34 - 39 Chapter 6: Outer, Dwarf and Exoplanets Pages: 41-54 Workbook Pages 37 - 48 Jupiter: Pages 41 - 42 Saturn: Pages 42 - 44 Uranus: Pages 44 - 45 Neptune: Pages 45 - 46 Dwarf Planets, Plutoids and Exoplanets: Pages 47 -54 3 Chapter 7: The Moons: Pages: 55 - 66 Workbook Pages 49 - 56 Chapter 8: Rocks and Ice: -
Stellar Magnetic Activity – Star-Planet Interactions
EPJ Web of Conferences 101, 005 02 (2015) DOI: 10.1051/epjconf/2015101005 02 C Owned by the authors, published by EDP Sciences, 2015 Stellar magnetic activity – Star-Planet Interactions Poppenhaeger, K.1,2,a 1 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambrigde, MA 02138, USA 2 NASA Sagan Fellow Abstract. Stellar magnetic activity is an important factor in the formation and evolution of exoplanets. Magnetic phenomena like stellar flares, coronal mass ejections, and high- energy emission affect the exoplanetary atmosphere and its mass loss over time. One major question is whether the magnetic evolution of exoplanet host stars is the same as for stars without planets; tidal and magnetic interactions of a star and its close-in planets may play a role in this. Stellar magnetic activity also shapes our ability to detect exoplanets with different methods in the first place, and therefore we need to understand it properly to derive an accurate estimate of the existing exoplanet population. I will review recent theoretical and observational results, as well as outline some avenues for future progress. 1 Introduction Stellar magnetic activity is an ubiquitous phenomenon in cool stars. These stars operate a magnetic dynamo that is fueled by stellar rotation and produces highly structured magnetic fields; in the case of stars with a radiative core and a convective outer envelope (spectral type mid-F to early-M), this is an αΩ dynamo, while fully convective stars (mid-M and later) operate a different kind of dynamo, possibly a turbulent or α2 dynamo. These magnetic fields manifest themselves observationally in a variety of phenomena. -
Rev 06/2018 ASTRONOMY EXAM CONTENT OUTLINE the Following
ASTRONOMY EXAM INFORMATION CREDIT RECOMMENDATIONS This exam was developed to enable schools to award The American Council on Education’s College credit to students for knowledge equivalent to that learned Credit Recommendation Service (ACE CREDIT) by students taking the course. This examination includes has evaluated the DSST test development history of the Science of Astronomy, Astrophysics, process and content of this exam. It has made the Celestial Systems, the Science of Light, Planetary following recommendations: Systems, Nature and Evolution of the Sun and Stars, Galaxies and the Universe. Area or Course Equivalent: Astronomy Level: 3 Lower Level Baccalaureate The exam contains 100 questions to be answered in 2 Amount of Credit: 3 Semester Hours hours. Some of these are pretest questions that will not Minimum Score: 400 be scored. Source: www.acenet.edu Form Codes: SQ500, SR500 EXAM CONTENT OUTLINE The following is an outline of the content areas covered in the examination. The approximate percentage of the examination devoted to each content area is also noted. I. Introduction to the Science of Astronomy – 5% a. Nature and methods of science b. Applications of scientific thinking c. History of early astronomy II. Astrophysics - 15% a. Kepler’s laws and orbits b. Newtonian physics and gravity c. Relativity III. Celestial Systems – 10% a. Celestial motions b. Earth and the Moon c. Seasons, calendar and time keeping IV. The Science of Light – 15% a. The electromagnetic spectrum b. Telescopes and the measurement of light c. Spectroscopy d. Blackbody radiation V. Planetary Systems: Our Solar System and Others– 20% a. Contents of our solar system b. -
The Formation of Brown Dwarfs 459
Whitworth et al.: The Formation of Brown Dwarfs 459 The Formation of Brown Dwarfs: Theory Anthony Whitworth Cardiff University Matthew R. Bate University of Exeter Åke Nordlund University of Copenhagen Bo Reipurth University of Hawaii Hans Zinnecker Astrophysikalisches Institut, Potsdam We review five mechanisms for forming brown dwarfs: (1) turbulent fragmentation of molec- ular clouds, producing very-low-mass prestellar cores by shock compression; (2) collapse and fragmentation of more massive prestellar cores; (3) disk fragmentation; (4) premature ejection of protostellar embryos from their natal cores; and (5) photoerosion of pre-existing cores over- run by HII regions. These mechanisms are not mutually exclusive. Their relative importance probably depends on environment, and should be judged by their ability to reproduce the brown dwarf IMF, the distribution and kinematics of newly formed brown dwarfs, the binary statis- tics of brown dwarfs, the ability of brown dwarfs to retain disks, and hence their ability to sustain accretion and outflows. This will require more sophisticated numerical modeling than is presently possible, in particular more realistic initial conditions and more realistic treatments of radiation transport, angular momentum transport, and magnetic fields. We discuss the mini- mum mass for brown dwarfs, and how brown dwarfs should be distinguished from planets. 1. INTRODUCTION form a smooth continuum with those of low-mass H-burn- ing stars. Understanding how brown dwarfs form is there- The existence of brown dwarfs was first proposed on the- fore the key to understanding what determines the minimum oretical grounds by Kumar (1963) and Hayashi and Nakano mass for star formation. In section 3 we review the basic (1963). -
Chapter 16 the Sun and Stars
Chapter 16 The Sun and Stars Stargazing is an awe-inspiring way to enjoy the night sky, but humans can learn only so much about stars from our position on Earth. The Hubble Space Telescope is a school-bus-size telescope that orbits Earth every 97 minutes at an altitude of 353 miles and a speed of about 17,500 miles per hour. The Hubble Space Telescope (HST) transmits images and data from space to computers on Earth. In fact, HST sends enough data back to Earth each week to fill 3,600 feet of books on a shelf. Scientists store the data on special disks. In January 2006, HST captured images of the Orion Nebula, a huge area where stars are being formed. HST’s detailed images revealed over 3,000 stars that were never seen before. Information from the Hubble will help scientists understand more about how stars form. In this chapter, you will learn all about the star of our solar system, the sun, and about the characteristics of other stars. 1. Why do stars shine? 2. What kinds of stars are there? 3. How are stars formed, and do any other stars have planets? 16.1 The Sun and the Stars What are stars? Where did they come from? How long do they last? During most of the star - an enormous hot ball of gas day, we see only one star, the sun, which is 150 million kilometers away. On a clear held together by gravity which night, about 6,000 stars can be seen without a telescope. -
Surfing on a Flash of Light from an Exploding Star ______By Abraham Loeb on December 26, 2019
Surfing on a Flash of Light from an Exploding Star _______ By Abraham Loeb on December 26, 2019 A common sight on the beaches of Hawaii is a crowd of surfers taking advantage of a powerful ocean wave to reach a high speed. Could extraterrestrial civilizations have similar aspirations for sailing on a powerful flash of light from an exploding star? A light sail weighing less than half a gram per square meter can reach the speed of light even if it is separated from the exploding star by a hundred times the distance of the Earth from the Sun. This results from the typical luminosity of a supernova, which is equivalent to a billion suns shining for a month. The Sun itself is barely capable of accelerating an optimally designed sail to just a thousandth of the speed of light, even if the sail starts its journey as close as ten times the Solar radius – the closest approach of the Parker Solar Probe. The terminal speed scales as the square root of the ratio between the star’s luminosity over the initial distance, and can reach a tenth of the speed of light for the most luminous stars. Powerful lasers can also push light sails much better than the Sun. The Breakthrough Starshot project aims to reach several tenths of the speed of light by pushing a lightweight sail for a few minutes with a laser beam that is ten million times brighter than sunlight on Earth (with ten gigawatt per square meter). Achieving this goal requires a major investment in building the infrastructure needed to produce and collimate the light beam.